Figure 2
From: A universal null-distribution for topological data analysis
The distribution of \(\pi\)-values in the Čech complex. We take the empirical CDFs of the \(\pi\)-values (log-scale), computed from various iid samples. The legend format is \(\mathcal {T}/ \mathbb {P}/ d / k\), where \(\mathcal {T}\) is the complex type, \(\mathbb {P}\) is the probability distribution, d is the dimension of the sampling space, and k is the degree of homology computed. By ‘box’, ‘torus’, ‘sphere’, ‘projective(-plane)’, and ‘Klein(-bottle)’ we refer to the uniform distribution on the respective space or its most natural parametrization, while ‘normal’ and ‘cauchy’ refer to the corresponding non-uniform distributions. See “Methods” and Sect. 3 in the Supplementary Information for further details.
